Ocular optical system

ABSTRACT

An ocular optical system for imaging of imaging rays entering an eye of an observer via the ocular optical system from a display screen is provided. A side facing towards the eye is an eye-side, and a side facing towards the display screen is a display-side. The ocular optical system includes a first lens element, a second lens element, and a third lens element from the eye-side to the display-side in order along an optical axis. The first lens element, the second lens element, and the third lens element each include an eye-side surface and a display-side surface. Lens elements having refracting power of the ocular optical system are only the first lens element, the second lens element, and the third lens element.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation application of and claims thepriority benefit of U.S. application Ser. No. 15/401,120, filed on Jan.9, 2017, now allowed, which claims the priority benefit of U.S.provisional application Ser. No. 62/396,242, filed on Sep. 19, 2016. Theentirety of each of the above-mentioned patent applications is herebyincorporated by reference herein and made a part of this specification.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The invention relates to an optical system, and particularly, to anocular optical system.

2. Description of Related Art

Virtual Reality (VR) refers to computer technologies used for simulatingand generating a three-dimensional virtual world, which enablesimmersive simulation for users by providing simulations pertaining tovisual sensation, auditory sensation and other sensations to users. Thecurrently existing VR devices are mainly focused on visual experiences.Binocular parallax of human eyes is simulated by separated images withtwo slightly different perspectives corresponding to the left and righteyes to achieve a stereo vision. In order to reduce the volume of the VRdevice so users can receive a magnified visual sensation from a smallerdisplay screen, an ocular optical system with magnifying capability isnow one of major topics in research and development for VR.

Because a half apparent field of view is smaller in the existing ocularoptical system, an observer may experience narrow vision, low resolutionand even aberrations so serious that an aberration compensation must beperformed on the display screen before presentation. Accordingly, how toincrease the half apparent field of view and enhance the imaging qualitybecomes one of issues to be addressed.

SUMMARY OF THE INVENTION

The invention is directed to an ocular optical system, which is capableof shortening a system length without sacrificing a favorable imagingquality and a large half apparent field of view.

Embodiments of the invention propose an ocular optical system forimaging of imaging rays entering an eye of an observer via the ocularoptical system from a display screen. A side facing towards the eye isan eye-side, and a side facing towards the display screen is adisplay-side. The ocular optical system includes a first lens element, asecond lens element, and a third lens element from the eye-side to thedisplay-side in order along an optical axis. The first lens element, thesecond lens element, and the third lens element each include an eye-sidesurface and a display-side surface.

In an embodiment of the invention, the first lens element has refractingpower. The second lens element has positive refracting power, and thedisplay-side surface of the second lens element has a concave portion ina vicinity of the optical axis. At least one of the eye-side surface andthe display-side surface of the third lens element is an asphericsurface.

In an embodiment of the invention, the first lens element has refractingpower. The eye-side surface of the second lens element has a convexportion in a vicinity of the optical axis. The display-side surface ofthe second lens element has a concave portion in a vicinity of theoptical axis. The third lens element has negative refracting power. Atleast one of the eye-side surface and the display-side surface of thethird lens element is an aspheric surface.

In an embodiment of the invention, the first lens element has refractingpower. The eye-side surface of the second lens element has a convexportion in a vicinity of the optical axis. The display-side surface ofthe second lens element has a concave portion in a vicinity of theoptical axis. The eye-side surface of the third lens element has aconcave portion in a vicinity of a periphery of the third lens element,and at least one of the eye-side surface and the display-side surface ofthe third lens element is an aspheric surface.

In an embodiment of the invention, the first lens element has positiverefracting power. The eye-side surface of the second lens element has aconvex portion in a vicinity of the optical axis. The display-sidesurface of the second lens element has a convex portion in a vicinity ofthe optical axis. The eye-side surface of the third lens element has aconvex portion in a vicinity of the optical axis.

In an embodiment of the invention, the first lens element has positiverefracting power. The eye-side surface of the second lens element has aconvex portion in a vicinity of a periphery of the second lens element.The display-side surface of the second lens element has a convex portionin a vicinity of the optical axis. The eye-side surface of the thirdlens element has a convex portion in a vicinity of the optical axis.

In an embodiment of the invention, the display-side surface of thesecond lens element has a convex portion in a vicinity of the opticalaxis. The third lens element has negative refracting power. The eye-sidesurface of the third lens element has a convex portion in a vicinity ofthe optical axis and a convex portion in a vicinity of a periphery ofthe third lens element.

In an embodiment of the invention, the display-side surface of thesecond lens element has a convex portion in a vicinity of the opticalaxis. The eye-side surface of the third lens element has a convexportion in a vicinity of the optical axis and a convex portion in avicinity of a periphery of the third lens element. The display-sidesurface of the third lens element has a concave portion in a vicinity ofthe optical axis.

In an embodiment of the invention, the display-side surface of thesecond lens element has a convex portion in a vicinity of the opticalaxis. The eye-side surface of the third lens element has a convexportion in a vicinity of the optical axis and a convex portion in avicinity of a periphery of the third lens element. The display-sidesurface of the third lens element has a concave portion in a vicinity ofa periphery of the third lens element.

In an embodiment of the invention, the second lens element has positiverefracting power. The eye-side surface of the second lens element has aconvex portion in a vicinity of the optical axis. The eye-side surfaceof the third lens element has a convex portion in a vicinity of theoptical axis. The display-side surface of the third lens element has aconcave portion in a vicinity of a periphery of the third lens element.

In an embodiment of the invention, the eye-side surface of the secondlens element has a convex portion in a vicinity of the optical axis. Thedisplay-side surface of the second lens element has a convex portion ina vicinity of the optical axis. The eye-side surface of the third lenselement has a convex portion in a vicinity of the optical axis. Thedisplay-side surface of the third lens element has a concave portion ina vicinity of a periphery of the third lens element.

In an embodiment of the invention, the eye-side surface of the secondlens element has a convex portion in a vicinity of the optical axis. Thedisplay-side surface of the second lens element has a convex portion ina vicinity of a periphery of the second lens element. The eye-sidesurface of the third lens element has a convex portion in a vicinity ofthe optical axis. The display-side surface of the third lens element hasa concave portion in a vicinity of a periphery of the third lenselement.

In an embodiment of the invention, the eye-side surface of the secondlens element has a convex portion in a vicinity of the optical axis. Thethird lens element has negative refracting power. The eye-side surfaceof the third lens element has a convex portion in a vicinity of theoptical axis. The display-side surface of the third lens element has aconcave portion in a vicinity of a periphery of the third lens element.

In an embodiment of the invention, the eye-side surface of the firstlens element has a concave portion in a vicinity of the optical axis.The display-side surface of the third lens element has a convex portionin a vicinity of a periphery of the third lens element.

In an embodiment of the invention, the eye-side surface of the firstlens element has a concave portion in a vicinity of the optical axis.The eye-side surface of the second lens element has a concave portion ina vicinity of a periphery of the second lens element.

In an embodiment of the invention, the eye-side surface of the firstlens element has a concave portion in a vicinity of the optical axis.The eye-side surface of the third lens element has a convex portion in avicinity of the optical axis.

In an embodiment of the invention, the eye-side surface of the firstlens element has a concave portion in a vicinity of the optical axis anda convex portion in a vicinity of a periphery of the first lens element.

In an embodiment of the invention, the eye-side surface of the firstlens element has a concave portion in a vicinity of the optical axis.The second lens element has negative refracting power.

In an embodiment of the invention, the eye-side surface of the firstlens element has a concave portion in a vicinity of the optical axis.The eye-side surface of the second lens element has a concave portion ina vicinity of the optical axis.

In an embodiment of the invention, the eye-side surface of the firstlens element has a concave portion in a vicinity of the optical axis.The third lens element has positive refracting power.

In an embodiment of the invention, the eye-side surface of the firstlens element has a concave portion in a vicinity of the optical axis.The eye-side surface of the third lens element has a convex portion in avicinity of a periphery of the third lens element.

In an embodiment of the invention, the eye-side surface of the secondlens element has a convex portion in a vicinity of the optical axis. Thedisplay-side surface of the second lens element has a concave portion ina vicinity of the optical axis. The eye-side surface of the third lenselement has a concave portion in a vicinity of the optical axis.

In an embodiment of the invention, the eye-side surface of the secondlens element has a convex portion in a vicinity of the optical axis. Theeye-side surface of the third lens element has a concave portion in avicinity of the optical axis. The display-side surface of the third lenselement has a convex portion in a vicinity of the optical axis.

Based on the above, in the embodiments of the invention, the ocularoptical system can provide the following advantageous effects. Withdesign and arrangement of the lens elements in terms of surface shapesand refracting powers as well as design of optical parameters, theocular optical system can include optical properties for overcoming theaberrations and provide the favorable imaging quality and the largeapparent field of view, given that the system length is shorten.

To make the above features and advantages of the invention morecomprehensible, several embodiments accompanied with drawings aredescribed in detail as follows.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the invention, and are incorporated in and constitute apart of this specification. The drawings illustrate embodiments of theinvention and, together with the description, serve to explain theprinciples of the invention.

FIG. 1 is a schematic view illustrating an ocular optical system.

FIG. 2 is a schematic view illustrating a surface structure of a lenselement.

FIG. 3 is a schematic view illustrating a concave and convex surfacestructure of a lens element and a ray focal point.

FIG. 4 is a schematic view illustrating a surface structure of a lenselement according to a first example.

FIG. 5 is a schematic view illustrating a surface structure of a lenselement according to a second example.

FIG. 6 is a schematic view illustrating a surface structure of a lenselement according to a third example.

FIG. 7 is a schematic view illustrating an ocular optical systemaccording to a first embodiment of the invention.

FIG. 8A to FIG. 8D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the firstembodiment of the invention.

FIG. 9 shows detailed optical data pertaining to the ocular opticalsystem according to the first embodiment of the invention.

FIG. 10 shows aspheric parameters pertaining to the ocular opticalsystem according to the first embodiment of the invention.

FIG. 11 is a schematic view illustrating an ocular optical systemaccording to a second embodiment of the invention.

FIG. 12A to FIG. 12D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the secondembodiment of the invention.

FIG. 13 shows detailed optical data pertaining to the ocular opticalsystem according to the second embodiment of the invention.

FIG. 14 shows aspheric parameters pertaining to the ocular opticalsystem according to the second embodiment of the invention.

FIG. 15 is a schematic view illustrating an ocular optical systemaccording to a third embodiment of the invention.

FIG. 16A to FIG. 16D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the thirdembodiment of the invention.

FIG. 17 shows detailed optical data pertaining to the ocular opticalsystem according to the third embodiment of the invention.

FIG. 18 shows aspheric parameters pertaining to the ocular opticalsystem according to the third embodiment of the invention.

FIG. 19 is a schematic view illustrating an ocular optical systemaccording to a fourth embodiment of the invention.

FIG. 20A to FIG. 20D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the fourthembodiment of the invention.

FIG. 21 shows detailed optical data pertaining to the ocular opticalsystem according to the fourth embodiment of the invention.

FIG. 22 shows aspheric parameters pertaining to the ocular opticalsystem according to the fourth embodiment of the invention.

FIG. 23 is a schematic view illustrating an ocular optical systemaccording to a fifth embodiment of the invention.

FIG. 24A to FIG. 24D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the fifthembodiment of the invention.

FIG. 25 shows detailed optical data pertaining to the ocular opticalsystem according to the fifth embodiment of the invention.

FIG. 26 shows aspheric parameters pertaining to the ocular opticalsystem according to the fifth embodiment of the invention.

FIG. 27 is a schematic view illustrating an ocular optical systemaccording to a sixth embodiment of the invention.

FIG. 28A to FIG. 28D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the sixthembodiment of the invention.

FIG. 29 shows detailed optical data pertaining to the ocular opticalsystem according to the sixth embodiment of the invention.

FIG. 30 shows aspheric parameters pertaining to the ocular opticalsystem according to the sixth embodiment of the invention.

FIG. 31 is a schematic view illustrating an ocular optical systemaccording to a seventh embodiment of the invention.

FIG. 32A to FIG. 32D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the seventhembodiment of the invention.

FIG. 33 shows detailed optical data pertaining to the ocular opticalsystem according to the seventh embodiment of the invention.

FIG. 34 shows aspheric parameters pertaining to the ocular opticalsystem according to the seventh embodiment of the invention.

FIG. 35 is a schematic view illustrating an ocular optical systemaccording to an eighth embodiment of the invention.

FIG. 36A to FIG. 36D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the eighthembodiment of the invention.

FIG. 37 shows detailed optical data pertaining to the ocular opticalsystem according to the eighth embodiment of the invention.

FIG. 38 shows aspheric parameters pertaining to the ocular opticalsystem according to the eighth embodiment of the invention.

FIG. 39 is a schematic view illustrating an ocular optical systemaccording to a ninth embodiment of the invention.

FIG. 40A to FIG. 40D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the ninthembodiment of the invention.

FIG. 41 shows detailed optical data pertaining to the ocular opticalsystem according to the ninth embodiment of the invention.

FIG. 42 shows aspheric parameters pertaining to the ocular opticalsystem according to the ninth embodiment of the invention.

FIG. 43 to FIG. 46 show important parameters and relation values thereofpertaining to the ocular optical system according to the first throughthe ninth embodiments of the invention.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to the present preferredembodiments of the invention, examples of which are illustrated in theaccompanying drawings. Wherever possible, the same reference numbers areused in the drawings and the description to refer to the same or likeparts.

In general, a ray direction of an ocular optical system V100 refers tothe following: imaging rays VI are emitted by a display screen V50,enter an eye V60 via the ocular optical system V100, and are thenfocused on a retina of the eye V60 for imaging and generating anenlarged virtual image VV at a least distance of distinct vision VD, asdepicted in FIG. 1. The following criteria for determining opticalspecifications of the present application are based on assumption that areversely tracking of the ray direction is parallel imaging rays passingthrough the ocular optical system from an eye-side and focused on thedisplay screen for imaging.

In the present specification, the description “a lens element havingpositive refracting power (or negative refracting power)” means that theparaxial refracting power of the lens element in Gaussian optics ispositive (or negative). The description “An eye-side (or display-side)surface of a lens element” only includes a specific region of thatsurface of the lens element where imaging rays are capable of passingthrough that region, namely the clear aperture of the surface. Theaforementioned imaging rays can be classified into two types, chief rayLc and marginal ray Lm. Taking a lens element depicted in FIG. 2 as anexample, I is an optical axis and the lens element is rotationallysymmetric, where the optical axis I is the axis of symmetry. The regionA of the lens element is defined as “a portion in a vicinity of theoptical axis”, and the region C of the lens element is defined as “aportion in a vicinity of a periphery of the lens element”. Besides, thelens element may also have an extending portion E extended radially andoutwardly from the region C, namely the portion outside of the clearaperture of the lens element. The extending portion E is usually usedfor physically assembling the lens element into an optical imaging lenssystem. Under normal circumstances, the imaging rays would not passthrough the extending portion E because those imaging rays only passthrough the clear aperture. The structures and shapes of theaforementioned extending portion E are only examples for technicalexplanation, the structures and shapes of lens elements should not belimited to these examples. Note that the extending portions of the lenselement surfaces depicted in the following embodiments are partiallyomitted.

The following criteria are provided for determining the shapes and theportions of lens element surfaces set forth in the presentspecification. These criteria mainly determine the boundaries ofportions under various circumstances including the portion in a vicinityof the optical axis, the portion in a vicinity of a periphery of a lenselement surface, and other types of lens element surfaces such as thosehaving multiple portions.

1. FIG. 2 is a radial cross-sectional view of a lens element. Beforedetermining boundaries of those aforesaid portions, two referentialpoints should be defined first, central point and transition point. Thecentral point of a surface of a lens element is a point of intersectionof that surface and the optical axis. The transition point is a point ona surface of a lens element, where the tangent line of that point isperpendicular to the optical axis. Additionally, if multiple transitionpoints appear on one single surface, then these transition points aresequentially named along the radial direction of the surface withnumbers starting from the first transition point. For instance, thefirst transition point (closest one to the optical axis), the secondtransition point, and the Nth transition point (farthest one to theoptical axis within the scope of the clear aperture of the surface). Theportion of a surface of the lens element between the central point andthe first transition point is defined as the portion in a vicinity ofthe optical axis. The portion located radially outside of the Nthtransition point (but still within the scope of the clear aperture) isdefined as the portion in a vicinity of a periphery of the lens element.In some embodiments, there are other portions existing between theportion in a vicinity of the optical axis and the portion in a vicinityof a periphery of the lens element; the numbers of portions depend onthe numbers of the transition point(s). In addition, the radius of theclear aperture (or a so-called effective radius) of a surface is definedas the radial distance from the optical axis I to a point ofintersection of the marginal ray Lm and the surface of the lens element.

2. Referring to FIG. 3, determining the shape of a portion is convex orconcave depends on whether a collimated ray passing through that portionconverges or diverges. That is, while applying a collimated ray to aportion to be determined in terms of shape, the collimated ray passingthrough that portion will be bended and the ray itself or its extensionline will eventually meet the optical axis. The shape of that portioncan be determined by whether the ray or its extension line meets(intersects) the optical axis (focal point) at the eye-side ordisplay-side. For instance, if the ray itself intersects the opticalaxis at the display-side of the lens element after passing through aportion, i.e. the focal point of this ray is at the display-side (seepoint R in FIG. 3), the portion will be determined as having a convexshape. On the contrary, if the ray diverges after passing through aportion, the extension line of the ray intersects the optical axis atthe eye-side of the lens element, i.e. the focal point of the ray is atthe eye-side (see point M in FIG. 3), that portion will be determined ashaving a concave shape. Therefore, referring to FIG. 3, the portionbetween the central point and the first transition point has a convexshape, the portion located radially outside of the first transitionpoint has a concave shape, and the first transition point is the pointwhere the portion having a convex shape changes to the portion having aconcave shape, namely the border of two adjacent portions.Alternatively, there is another common way for a person with ordinaryskill in the art to tell whether a portion in a vicinity of the opticalaxis has a convex or concave shape by referring to the sign of an “R”value, which is the (paraxial) radius of curvature of a lens surface.The R value which is commonly used in conventional optical designsoftware such as Zemax and Code V. The R value usually appears in thelens data sheet in the software. For an eye-side surface, positive Rmeans that the eye-side surface is convex, and negative R means that theeye-side surface is concave. Conversely, for a display-side surface,positive R means that the display-side surface is concave, and negativeR means that the display-side surface is convex. The result found byusing this method should be consistent as by using the other waymentioned above, which determines surface shapes by referring to whetherthe focal point of a collimated ray is at the eye-side or thedisplay-side.

3. For none transition point cases, the portion in a vicinity of theoptical axis is defined as the portion between 0˜50% of the effectiveradius (radius of the clear aperture) of the surface, whereas theportion in a vicinity of a periphery of the lens element is defined asthe portion between 50˜100% of effective radius (radius of the clearaperture) of the surface.

Referring to the first example depicted in FIG. 4, only one transitionpoint, namely a first transition point, appears within the clearaperture of the display-side surface of the lens element. Portion I is aportion in a vicinity of the optical axis, and portion II is a portionin a vicinity of a periphery of the lens element. The portion in avicinity of the optical axis is determined as having a concave surfacedue to the R value at the display-side surface of the lens element ispositive. The shape of the portion in a vicinity of a periphery of thelens element is different from that of the radially inner adjacentportion, i.e. the shape of the portion in a vicinity of a periphery ofthe lens element is different from the shape of the portion in avicinity of the optical axis; the portion in a vicinity of a peripheryof the lens element has a convex shape.

Referring to the second example depicted in FIG. 5, a first transitionpoint and a second transition point exist on the eye-side surface(within the clear aperture) of a lens element. In which portion I is theportion in a vicinity of the optical axis, and portion III is theportion in a vicinity of a periphery of the lens element. The portion ina vicinity of the optical axis has a convex shape because the R value atthe eye-side surface of the lens element is positive. The portion in avicinity of a periphery of the lens element (portion III) has a convexshape. What is more, there is another portion having a concave shapeexisting between the first and second transition point (portion II).

Referring to a third example depicted in FIG. 6, no transition pointexists on the eye-side surface of the lens element. In this case, theportion between 0˜50% of the effective radius (radius of the clearaperture) is determined as the portion in a vicinity of the opticalaxis, and the portion between 50˜100% of the effective radius isdetermined as the portion in a vicinity of a periphery of the lenselement. The portion in a vicinity of the optical axis of the eye-sidesurface of the lens element is determined as having a convex shape dueto its positive R value, and the portion in a vicinity of a periphery ofthe lens element is determined as having a convex shape as well.

FIG. 7 is a schematic view illustrating an ocular optical systemaccording to the first embodiment of the invention, and FIG. 8A to FIG.8D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the first embodiment of theinvention. Referring to FIG. 7, an ocular optical system 10 according tothe first embodiment of the invention is used for imaging of imagingrays entering an eye of an observer via the ocular optical system 10 anda pupil 2 of the eye of the observer from a display screen 100. A sidefacing towards the eye is an eye-side, a side facing towards the displayscreen 100 is a display-side. The ocular optical system 10 includes afirst lens element 3, a second lens element 4, and a third lens element5 from the eye-side to the display-side in order along an optical axis Iof the ocular optical system 10. When the rays emitted by the displayscreen 100 enter the ocular optical system 10, pass through third lenselement 5, the second lens elements 4, and the first lens element 3 inorder, and enter the eye of the observer via the pupil 2, an image isformed on a retina of the eye.

The first lens element 3, the second lens element 4, and the third lenselement 5 each include an eye-side surface 31, 41, 51 facing theeye-side and allowing the imaging rays to pass through and adisplay-side surface 32, 42, 52 facing the display-side and allowing theimaging rays to pass through. In order to meet the demand for lighterproducts, the first lens element 3, the second lens element 4, and thethird lens element 5 all have refracting power. Besides, the first lenselement 3, the second lens element 4, and the third lens element 5 aremade of plastic material; nevertheless, the material of the first lenselement 3, the second lens element 4, and the third lens element 5 isnot limited thereto.

The first lens element 3 has positive refracting power. The eye-sidesurface 31 of the first lens element 3 is a convex surface, and has aconvex portion 311 in a vicinity of the optical axis I and a convexportion 313 in a vicinity of a periphery of the first lens element 3.The display-side surface 32 of the first lens element 3 is a convexsurface, and has a convex portion 321 in a vicinity of the optical axisI and a convex portion 323 in a vicinity of a periphery of the firstlens element 3.

The second lens element 4 has positive refracting power. The eye-sidesurface 41 of the second lens element 4 is a convex surface, and has aconvex portion 411 in a vicinity of the optical axis I and a convexportion 413 in a vicinity of a periphery of the second lens element 4.The display-side surface 42 of the second lens element 4 is a convexsurface, and has a convex portion 421 in a vicinity of the optical axisI and a convex portion 423 in a vicinity of a periphery of the secondlens element 4.

The third lens element 5 has negative refracting power. The eye-sidesurface 51 of the third lens element 5 is a convex surface, and has aconvex portion 511 in a vicinity of the optical axis I and a convexportion 513 in a vicinity of a periphery of the third lens element 5.The display-side surface 52 of the third lens element 5 is a concavesurface, and has a concave portion 522 in a vicinity of the optical axisI and a concave portion 524 in a vicinity of a periphery of the thirdlens element 5.

Further, in the present embodiment, only the aforesaid lens elementshave refracting power, and the ocular optical system 10 includes onlythe three lens elements having the refracting power.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the first embodiment is indicated inFIG. 1, FIG. 43, and FIG. 44.

wherein

EPD represents an exit pupil diameter of the ocular optical system 10corresponding to a diameter of the pupil 2 of the observer, as depictedin FIG. 1;

EPSD represents a semidiameter of the pupil 2 of the observer;

ER (eye relief) represents an exit pupil distance, which is a distancefrom the pupil 2 of the observer to the first lens element 3 along theoptical axis I;

ω represents a half apparent field of view, which is one half the fieldof view of the observer, as depicted in FIG. 1;

T1 represents a thickness of the first lens element 3 along the opticalaxis I;

T2 represents a thickness of the second lens element 4 along the opticalaxis I;

T3 represents a thickness of the third lens element 5 along the opticalaxis I;

G12 represents a distance from the display-side surface 32 of the firstlens element 3 to the eye-side surface 41 of the second lens element 4along the optical axis I, which is an air gap from the first lenselement 3 to the second lens element 4 along the optical axis I;

G23 represents a distance from the display-side surface 42 of the secondlens element 4 to the eye-side surface 51 of the third lens element 5along the optical axis I, which is an air gap from the second lenselement 4 to the third lens element 5 along the optical axis I;

G3D represents a distance from the display-side surface 52 of the thirdlens element 5 to the display screen 100 along the optical axis I, whichis an air gap from the third lens element 5 to the display screen 100along the optical axis I;

DLD represents a diagonal length of the display screen 100 correspondingto one single pupil 2 of the observer, as depicted in FIG. 1;

a least distance of distinct vision is the closest distance that the eyeis able to clearly focus on, which is normally 250 millimeters (mm) foryoung people, i.e., the least distance of distinct vision VD depicted inFIG. 1;

ALT represents a sum of the thicknesses of the first lens element 3, thesecond lens element 4, and the third lens element 5 along the opticalaxis I, i.e., a sum of T1, T2, and T3;

Gaa represents a sum of two air gaps from the first lens element to thethird lens element along the optical axis, i.e., a sum of G12 and G23;

TTL represents a distance from the eye-side surface 31 of the first lenselement 3 to the display screen 100 along the optical axis I;

TL represents a distance from the eye-side surface 31 of the first lenselement 3 to the display-side surface 52 of the third lens element 5along the optical axis I;

SL represents a system length, which is a distance from the pupil 2 ofthe observer to the display screen 100 along the optical axis I; and

EFL represents an effective focal length of the ocular optical system10.

Besides, it is further defined that:

f1 is a focal length of the first lens element 3;

f2 is a focal length of the second lens element 4;

f3 is a focal length of the third lens element 5;

n1 is a refractive index of the first lens element 3;

n2 is a refractive index of the second lens element 4;

n3 is a refractive index of the third lens element 5;

v1 is an Abbe number of the first lens element 3, and the Abbe number isalso known as a dispersion coefficient;

v2 is an Abbe number of the second lens element 4;

v3 is an Abbe number of the third lens element 5;

D1 is a diameter of a clear aperture of the eye-side surface 31 of thefirst lens element 3;

D2 is a diameter of a clear aperture of the eye-side surface 41 of thesecond lens element 4; and

D3 is a diameter of a clear aperture of the eye-side surface 51 of thethird lens element 5.

Other detailed optical data in the first embodiment are indicated inFIG. 9. In the first embodiment, the effective focal length (EFL) (i.e.system focal length) of the ocular optical system 10 is 48.594 mm, thehalf apparent field of view (ω) thereof is 40.000°, TTL thereof is56.100 mm, and an f-number (Fno) thereof is 9.626. Specifically, the“Fno” referred to in this specification is calculated based on theprinciple of light reversibility, in which the eye-side is considered asan object-side, the display-side is considered as an image-side, and thepupil of the eye of the observer is considered as a pupil of incidentlight. Moreover, 0.5 times DLD thereof is 40.459 mm. Among them, theeffective radius in FIG. 9 refers to one half the diameter of the clearaperture.

Further, in the present embodiment, the eye-side surface 31 and thedisplay-side surface 32 of the first lens element 3 and the eye-sidesurface 51 and the display-side surface 52 of the third lens element 5(four surfaces in total) are the aspheric surfaces, and the eye-sidesurface 41 and the display-side surface 42 of the second lens element 4are spherical surfaces. The aspheric surfaces are defined by thefollowing formula.

$\begin{matrix}{{Z(y)} = {{\frac{Y^{2}}{R}/\left( {1 + \sqrt{1 - {\left( {1 + K} \right)\frac{Y^{2}}{R^{2}}}}} \right)} + {\sum\limits_{i = 1}^{n}{a_{i} \times Y^{i}}}}} & (1)\end{matrix}$

wherein

Y: a distance from a point on an aspheric curve to the optical axis I;

Z: a depth of the aspheric surface (a vertical distance between thepoint on the aspheric surface that is spaced from the optical axis I bythe distance Y and a tangent plane tangent to a vertex of the asphericsurface on the optical axis I);

R: a radius of curvature of the surface of the lens element close to theoptical axis I;

K: a conic constant;

α_(i): the i^(th) aspheric coefficient.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 10. In FIG. 10, the referential number 31 is one rowthat represents the aspheric coefficient of the eye-side surface 31 ofthe first lens element 3, and the reference numbers in other rows can bededuced from the above. In FIG. 10, the aspheric coefficients of theeye-side surface 41 and the display-side surface 42 are all zero, whichmeans that the eye-side surface 41 and the display-side surface 42 arespherical surfaces.

Referring to FIG. 8A to FIG. 8D, FIG. 8A to FIG. 8D illustrate theaberrations of the ocular optical system 10 of the first embodiment,which are the aberrations obtained based on the assumption that thereversely tracking of the ray direction is the parallel imaging rayspassing through the pupil 2 and the ocular optical system 10 in orderfrom the eye-side and focused on the display screen 100 for imaging. Inthe present embodiment, each aberration behavior shown in each of theaberrations can decide the corresponding aberration behavior for imagingof the imaging rays from the display screen 100 on the retina of the eyeof the observer. In other words, when each aberration behavior in eachof the aberrations is smaller, each aberration behavior for imaging onthe retina of the eye of the observer may also be smaller so the imagewith better imaging quality can be observed by the observer. FIG. 8Aillustrates the longitudinal spherical aberration when a pupil radiusthereof is 2.5000 mm and when wavelengths are 450 nm, 540 nm and 630 nmin the first embodiment. FIG. 8B and FIG. 8C illustrate a fieldcurvature aberration in a sagittal direction and a field curvatureaberration in a tangential direction on the display screen 100 whenwavelengths are 450 nm, 540 nm and 630 nm in the first embodiment. FIG.8D illustrates a distortion aberration on the display screen 100 whenwavelengths are 450 nm, 540 nm and 630 nm in the first embodiment. InFIG. 8A which illustrates the longitudinal spherical aberration in thefirst embodiment, the curve of each wavelength is close to one anotherand approaches the center position, which indicates that the off-axisray of each wavelength at different heights is concentrated around theimaging point. The skew margin of the curve of each wavelength indicatesthat the imaging point deviation of the off-axis ray at differentheights is controlled within a range of ±1 mm. Hence, it is evident thatthe spherical aberration of the same wavelength can be significantlyimproved according to the present embodiment. In addition, the curves ofthe three representative wavelengths (red, green, and blue) are close toone another, which indicates that the imaging positions of the rays withdifferent wavelengths are rather concentrated; therefore, the chromaticaberration can be significantly improved as well.

In FIG. 8B and FIG. 8C which illustrate two diagrams of field curvatureaberrations, the focal length variation of the three representativewavelengths within the entire field of view falls within the range of±5.9 mm, which indicates that aberration of the optical system providedin the first embodiment can be effectively eliminated. In FIG. 8D, thediagram of distortion aberration shows that the distortion aberration inthe first embodiment can be maintained within the range of ±2.2%, whichindicates that the distortion aberration in the first embodiment cancomply with the imaging quality requirement of the optical system.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the first embodiment can have the favorableimaging quality, given that TTL thereof is shortened to about 56.100 mm.As a result, according to the first embodiment, the length of theoptical system can be shortened and the apparent field of view can beenlarged without sacrificing the favorable optical properties. In thisway, the product design with miniaturization, low aberration and largeapparent field of view taken into account can be realized.

FIG. 11 is a schematic view illustrating an ocular optical systemaccording to the second embodiment of the invention, and FIG. 12A toFIG. 12D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the secondembodiment of the invention. With reference to FIG. 11, the ocularoptical system 10 according to the second embodiment of the invention issimilar to that provided in the first embodiment, while the differencestherebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3, 4, and 5 inthese two embodiments are different to some extent. Further, in thepresent embodiment, the eye-side surface 31 of the first lens element 3is a concave surface, and has a concave portion 312 in a vicinity of theoptical axis I and a concave portion 314 in a vicinity of a periphery ofthe first lens element 3. The second lens element 4 has negativerefracting power. The eye-side surface 41 of the second lens element 4is a concave surface, and has a concave portion 412 in a vicinity of theoptical axis I and a concave portion 414 in a vicinity of a periphery ofthe second lens element 4. The display-side surface 42 of the secondlens element 4 is a plane surface, and has a plane portion 425 in avicinity of the optical axis I and a plane portion 426 in a vicinity ofa periphery of the second lens element 4. The third lens element 5 haspositive refracting power. Moreover, in the present embodiment, thedisplay-side surface 52 of the third lens element 5 is a convex surface,and has a convex portion 521 in a vicinity of the optical axis I and aconvex portion 523 in a vicinity of a periphery of the third lenselement 5. For clear illustration, it should be mentioned that the samereference numbers of the concave portions and the convex portions in thetwo embodiments are omitted from FIG. 11. In this embodiment, all theeye-side surfaces 31, 41, and 51 and all the display-side surfaces 32,42, and 52 are spherical surfaces.

Detailed optical data of the ocular optical system 10 in the secondembodiment are indicated in FIG. 13. In the second embodiment, EFL ofthe ocular optical system 10 is 44.658 mm, ω thereof is 45.000°, TTLthereof is 57.500 mm, Fno thereof is 8.864, and 0.5 times DLD thereof is31.563 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 14 according to the second embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the second embodiment is indicated inFIG. 43 and FIG. 44.

In FIG. 12A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.5000 mm according to the second embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±2 mm. In FIG. 12B and FIG. 12C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±17 mm. In FIG. 12D, the diagramof distortion aberration shows that the distortion aberration in thesecond embodiment can be maintained within the range of ±30%.Accordingly, compared to the existing ocular optical system, the secondembodiment can have the favorable imaging quality, given that TTL isshortened to about 57.500 mm.

According to the above description, compared to the first embodiment,the advantages of the second embodiment are as follows. Fno of thesecond embodiment is less than that of the first embodiment. ω of thesecond embodiment is greater than that of the first embodiment.

FIG. 15 is a schematic view illustrating an ocular optical systemaccording to the third embodiment of the invention, and FIG. 16A to FIG.16D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the third embodiment of theinvention. With reference to FIG. 15, the ocular optical system 10according to the third embodiment of the invention is similar to thatprovided in the first embodiment, while the differences therebetween areas follows. The optical data, the aspheric coefficients, and theparameters of the lens elements 3, 4, and 5 in these two embodiments aredifferent to some extent. Further, in the present embodiment, theeye-side surface 31 of the first lens element 3 has a concave portion312 in a vicinity of the optical axis I and a concave portion 314 in avicinity of a periphery of the first lens element 3. The eye-sidesurface 41 of the second lens element 4 has a convex portion 411 in avicinity of the optical axis I and a concave portion 414 in a vicinityof a periphery of the second lens element 4. The display-side surface 42of the second lens element 4 has a concave portion 422 in a vicinity ofthe optical axis I and a convex portion 423 in a vicinity of a peripheryof the second lens element 4. The eye-side surface 51 of the third lenselement 5 has a convex portion 511 in a vicinity of the optical axis Iand a concave portion 514 in a vicinity of a periphery of the third lenselement 5. The display-side surface 52 of the third lens element 5 has aconcave portion 522 in a vicinity of the optical axis I and a convexportion 523 in a vicinity of a periphery of the third lens element 5.For clear illustration, it should be mentioned that the same referencenumbers of the concave portions and the convex portions in the twoembodiments are omitted from FIG. 15. In this embodiment, all theeye-side surfaces 31, 41, and 51 and all the display-side surfaces 32,42, and 52 are aspheric surfaces.

Detailed optical data of the ocular optical system 10 in the thirdembodiment are indicated in FIG. 17. In the third embodiment, EFL of theocular optical system 10 is 48.338 mm, ω thereof is 45.000°, TTL thereofis 53.228 mm, Fno thereof is 8.024, and 0.5 times DLD thereof is 35.333mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 18 according to the third embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the third embodiment is indicated inFIG. 43 and FIG. 44.

In FIG. 16A which illustrates the longitudinal spherical aberration whenthe pupil radius is 3.0000 mm according to the third embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.6 mm. In FIG. 16B and FIG. 16C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±1.5 mm. In FIG. 16D, thediagram of distortion aberration shows that the distortion aberration inthe third embodiment can be maintained within the range of ±28%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the third embodiment can have the favorableimaging quality, given that the TTL is shortened to about 53.228 mm.

According to the above description, compared to the first embodiment,the advantages of the third embodiment are as follows. The TTL of theocular optical system 10 in the third embodiment is less than the TTL inthe first embodiment; Fno of the third embodiment is less than that ofthe first embodiment; the half apparent field of view ω in the thirdembodiment is greater than the half apparent field of view ω in thefirst embodiment. The longitudinal spherical aberration of the thirdembodiment is less than that of the first embodiment. The fieldcurvature of the third embodiment is less than that of the firstembodiment.

FIG. 19 is a schematic view illustrating an ocular optical systemaccording to the fourth embodiment of the invention, and FIG. 20A toFIG. 20D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the fourthembodiment of the invention. With reference to FIG. 19, the ocularoptical system 10 according to the fourth embodiment of the invention issimilar to that provided in the first embodiment, while differencestherebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3, 4, and 5 inthese two embodiments are different to some extent. Further, in thepresent embodiment, the eye-side surface 41 of the second lens element 4has a convex portion 411 in a vicinity of the optical axis I and aconcave portion 414 in a vicinity of a periphery of the second lenselement 4. The display-side surface 42 of the second lens element 4 hasa concave portion 422 in a vicinity of the optical axis I and a convexportion 423 in a vicinity of a periphery of the second lens element 4.The eye-side surface 51 of the third lens element 5 is a concavesurface, and has a concave portion 512 in a vicinity of the optical axisI and a concave portion 514 in a vicinity of a periphery of the thirdlens element 5. The display-side surface 52 of the third lens element 5is a convex surface, and has a convex portion 521 in a vicinity of theoptical axis I and a convex portion 523 in a vicinity of a periphery ofthe third lens element 5. For clear illustration, it should be mentionedthat the same reference numbers of the concave portions and the convexportions in the two embodiments are omitted from FIG. 19. In thisembodiment, all the eye-side surfaces 31, 41, and 51 and all thedisplay-side surfaces 32, 42, and 52 are aspheric surfaces.

Detailed optical data of the ocular optical system 10 in the fourthembodiment are indicated in FIG. 21. In the fourth embodiment, EFL ofthe ocular optical system 10 is 49.996 mm, ω thereof is 45.000°, TTLthereof is 61.224 mm, Fno thereof is 12.430, and 0.5 times DLD thereofis 35.638 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 22 according to the fourth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the fourth embodiment is indicated inFIG. 43 and FIG. 44.

In FIG. 20A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm and when wavelengths are 486 nm, 587 nmand 656 nm according to the fourth embodiment, the imaging pointdeviation of the off-axis ray at different heights is controlled withina range of ±0.65 mm. In FIG. 20B and FIG. 20C which illustrate twodiagrams of field curvature aberrations when wavelengths are 486 nm, 587nm, and 656 nm, the focal length variation of the three representativewavelengths within the entire field of view falls within the range of±1.1 mm. In FIG. 20D, the diagram of distortion aberration shows thatthe distortion aberration in the fourth embodiment can be maintainedwithin the range of ±29%. Accordingly, compared to the existing ocularoptical system, the ocular optical system provided in the fourthembodiment can have the favorable imaging quality, given that TTL isshortened to about 61.224 mm.

According to the above description, compared to the first embodiment,the advantages of the fourth embodiment are as follows. ω of the fourthembodiment is greater than that of the first embodiment. Thelongitudinal spherical aberration of the fourth embodiment is less thanthat of the first embodiment. The field curvature of the fourthembodiment is less than that of the first embodiment. Because athickness difference between portions in a vicinity of the optical axisand in a vicinity of a periphery of the lens element in the fourthembodiment is less than that of the first embodiment, the ocular opticalsystem in the fourth embodiment is, in comparison with that provided inthe first embodiment, easier to be manufactured and thus has higheryield.

FIG. 23 is a schematic view illustrating an ocular optical systemaccording to the fifth embodiment of the invention, and FIG. 24A to FIG.24D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the fifth embodiment of theinvention. With reference to FIG. 23, the ocular optical system 10according to the fifth embodiment of the invention is similar to thatprovided in the first embodiment, while the differences are as follows.The optical data, the aspheric coefficients, and the parameters of thelens elements 3, 4, and 5 in these two embodiments are different to someextent. Further, in the present embodiment, the eye-side surface 41 ofthe second lens element 4 has a convex portion 411 in a vicinity of theoptical axis I and a concave portion 414 in a vicinity of a periphery ofthe second lens element 4. The display-side surface 42 of the secondlens element 4 has a concave portion 422 in a vicinity of the opticalaxis I and a convex portion 423 in a vicinity of a periphery of thesecond lens element 4. The eye-side surface 51 of the third lens element5 is a concave surface, and has a concave portion 512 in a vicinity ofthe optical axis I and a concave portion 514 in a vicinity of aperiphery of the third lens element 5. The display-side surface 52 ofthe third lens element 5 is a convex surface, and has a convex portion521 in a vicinity of the optical axis I and a convex portion 523 in avicinity of a periphery of the third lens element 5. For clearillustration, it should be mentioned that the same reference numbers ofthe concave portions and the convex portions in the two embodiments areomitted from FIG. 23. In this embodiment, all the eye-side surfaces 31,41, and 51 and all the display-side surfaces 32, 42, and 52 are asphericsurfaces.

Detailed optical data of the ocular optical system 10 in the fifthembodiment are indicated in FIG. 25. In the fifth embodiment, EFL of theocular optical system 10 is 50.117 mm, ω thereof is 45.000°, TTL thereofis 61.318 mm, Fno thereof is 12.460, and 0.5 times DLD thereof is 35.857mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 26 according to the fifth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the fifth embodiment is indicated inFIG. 43 and FIG. 44.

In FIG. 24A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the fifth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.62 mm. In FIG. 24B and FIG. 24C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±1.2 mm. In FIG. 24D, thediagram of distortion aberration shows that the distortion aberration inthe fifth embodiment can be maintained within the range of ±29%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the fifth embodiment can have the favorableimaging quality, given that the TTL is shortened to about 61.318 mm.

According to the above description, compared to the first embodiment,the advantages of the fifth embodiment are as follows. ω of the fifthembodiment is less than that of the first embodiment. The longitudinalspherical aberration of the fifth embodiment is less than that of thefirst embodiment. The field curvature of the fifth embodiment is lessthan that of the first embodiment. Because a thickness differencebetween portions in a vicinity of the optical axis and in a vicinity ofa periphery of the lens element in the fifth embodiment is less thanthat of the first embodiment, the ocular optical system in the fifthembodiment is, in comparison with that provided in the first embodiment,easier to be manufactured and thus has higher yield.

FIG. 27 is a schematic view illustrating an ocular optical systemaccording to the sixth embodiment of the invention, and FIG. 28A to FIG.28D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the sixth embodiment of theinvention. With reference to FIG. 27, the ocular optical system 10according to the sixth embodiment of the invention is similar to thatprovided in the first embodiment, while the differences therebetween areas follows. The optical data, the aspheric coefficients, and theparameters of the lens elements 3, 4, and 5 in these two embodiments aredifferent to some extent. The display-side surface 42 of the second lenselement 4 is a concave surface, and has a concave portion 422 in avicinity of the optical axis I and a concave portion 424 in a vicinityof a periphery of the second lens element 4. The eye-side surface 51 ofthe third lens element 5 is a concave surface, and has a concave portion512 in a vicinity of the optical axis I and a concave portion 514 in avicinity of a periphery of the third lens element 5. The display-sidesurface 52 of the third lens element 5 is a convex surface, and has aconvex portion 521 in a vicinity of the optical axis I and a convexportion 523 in a vicinity of a periphery of the third lens element 5.For clear illustration, it should be mentioned that the same referencenumbers of the concave portions and the convex portions in the twoembodiments are omitted from FIG. 27. In this embodiment, all theeye-side surfaces 31, 41, and 51 and all the display-side surfaces 32,42, and 52 are aspheric surfaces.

Detailed optical data of the ocular optical system 10 in the sixthembodiment are indicated in FIG. 29. In the sixth embodiment, EFL of theocular optical system 10 is 50.272 mm, ω thereof is 45.000°, TTL thereofis 62.697 mm, Fno thereof is 8.306, and 0.5 times DLD thereof is 35.286mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 30 according to the sixth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the sixth embodiment is indicated inFIG. 45 and FIG. 46.

In FIG. 28A which illustrates the longitudinal spherical aberration whenthe pupil radius is 3.0000 mm according to the sixth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±135 mm. In FIG. 28B and FIG. 28C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±1.2 mm. In FIG. 28D, thediagram of distortion aberration shows that the distortion aberration inthe sixth embodiment can be maintained within the range of ±21%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the sixth embodiment can have the favorableimaging quality, given that TTL is shortened to about 62.697 mm.

According to the above description, compared to the first embodiment,the advantages of the sixth embodiment are as follows. Fno of the sixthembodiment is less than that of the first embodiment. ω of the sixthembodiment is less than that of the first embodiment. The fieldcurvature of the sixth embodiment is less than that of the firstembodiment. Because a thickness difference between portions in avicinity of the optical axis and in a vicinity of a periphery of thelens element in the sixth embodiment is less than that of the firstembodiment, the ocular optical system in the sixth embodiment is, incomparison with that provided in the first embodiment, easier to bemanufactured and thus has higher yield.

FIG. 31 is a schematic view illustrating an ocular optical systemaccording to the seventh embodiment of the invention, and FIG. 32A toFIG. 32D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the seventhembodiment of the invention. With reference to FIG. 31, the ocularoptical system 10 according to the seventh embodiment of the inventionis similar to that provided in the first embodiment, while thedifferences therebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3, 4, and 5 inthese two embodiments are different to some extent. The eye-side surface41 of the second lens element 4 has a convex portion 411 in a vicinityof the optical axis I and a concave portion 414 in a vicinity of aperiphery of the second lens element 4. The display-side surface 42 ofthe second lens element 4 has a concave portion 422 in a vicinity of theoptical axis I and a convex portion 423 in a vicinity of a periphery ofthe second lens element 4. The eye-side surface 51 of the third lenselement 5 is a concave surface, and has a concave portion 512 in avicinity of the optical axis I and a concave portion 514 in a vicinityof a periphery of the third lens element 5. The display-side surface 52of the third lens element 5 is a convex surface, and has a convexportion 521 in a vicinity of the optical axis I and a convex portion 523in a vicinity of a periphery of the third lens element 5. For clearillustration, it should be mentioned that the same reference numbers ofthe concave portions and the convex portions in the two embodiments areomitted from FIG. 31. In this embodiment, all the eye-side surfaces 31,41, and 51 and all the display-side surfaces 32, 42, and 52 are asphericsurfaces.

Detailed optical data of the ocular optical system 10 in the seventhembodiment are indicated in FIG. 33. In the seventh embodiment, EFL ofthe ocular optical system 10 is 50.090 mm, ω thereof is 45.000°, TTLthereof is 63.000 mm, Fno thereof is 8.225, and 0.5 times DLD thereof is35.192 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 34 according to the seventh embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the seventh embodiment is indicatedin FIG. 45 and FIG. 46.

In FIG. 32A which illustrates the longitudinal spherical aberration whenthe pupil radius is 3.0000 mm according to the seventh embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±1.1 mm. In FIG. 32B and FIG. 32C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±0.9 mm. In FIG. 32D, thediagram of distortion aberration shows that the distortion aberration inthe seventh embodiment can be maintained within the range of ±30%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the seventh embodiment can have the favorableimaging quality, given that the TTL is shortened to about 63.000 mm.

According to the above description, compared to the first embodiment,the advantages of the seventh embodiment are as follows. Fno of theseventh embodiment is less than that of the first embodiment. ω of theseventh embodiment is less than that of the first embodiment. The fieldcurvature of the seventh embodiment is less than that of the firstembodiment. Besides, because a thickness difference between portions ina vicinity of the optical axis and in a vicinity of a periphery of thelens element in the seventh embodiment is less than that of the firstembodiment, the ocular optical system in the seventh embodiment is, incomparison with that provided in the first embodiment, easier to bemanufactured and thus has higher yield.

FIG. 35 is a schematic view illustrating an ocular optical systemaccording to the eighth embodiment of the invention, and FIG. 36A toFIG. 36D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the eighthembodiment of the invention. With reference to FIG. 35, the ocularoptical system 10 according to the eighth embodiment of the invention issimilar to that provided in the first embodiment, while the differencestherebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3, 4, and 5 inthese two embodiments are different to some extent. Further, in thepresent embodiment, the eye-side surface 31 of the first lens element 3is a concave surface, and has a concave portion 312 in a vicinity of theoptical axis I and a concave portion 314 in a vicinity of a periphery ofthe first lens element 3. The display-side surface 42 of the second lenselement 4 has a concave portion 422 in a vicinity of the optical axis Iand a convex portion 423 in a vicinity of a periphery of the second lenselement 4. The eye-side surface 51 of the third lens element 5 is aconcave surface, and has a concave portion 512 in a vicinity of theoptical axis I and a concave portion 514 in a vicinity of a periphery ofthe third lens element 5. The display-side surface 52 of the third lenselement 5 is a convex surface, and has a convex portion 521 in avicinity of the optical axis I and a convex portion 523 in a vicinity ofa periphery of the third lens element 5. For clear illustration, itshould be mentioned that the same reference numbers of the concaveportions and the convex portions in the two embodiments are omitted fromFIG. 35. In this embodiment, all the eye-side surfaces 31, 41, and 51and all the display-side surfaces 32, 42, and 52 are aspheric surfaces.

Detailed optical data of the ocular optical system 10 in the eighthembodiment are indicated in FIG. 37. In the eighth embodiment, EFL ofthe ocular optical system 10 is 50.327 mm, ω thereof is 45.000°, TTLthereof is 63.000 mm, Fno thereof is 8.092, and 0.5 times DLD thereof is34.974 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 38 according to the eighth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the eighth embodiment is indicated inFIG. 45 and FIG. 46.

In FIG. 36A which illustrates the longitudinal spherical aberration whenthe pupil radius is 3.0000 mm according to the eighth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±1.35 mm. In FIG. 36B and FIG. 36C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±0.98 mm. In FIG. 36D, thediagram of distortion aberration shows that the distortion aberration inthe eighth embodiment can be maintained within the range of ±30%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the eighth embodiment can have the favorableimaging quality, given that the TTL is shortened to about 63.000 mm.

According to the above description, compared to the first embodiment,the advantages of the eighth embodiment are as follows. Fno of theeighth embodiment is less than that of the first embodiment. ω of theeighth embodiment is greater than that of the first embodiment. Thefield curvature of the eighth embodiment is less than that of the firstembodiment. Besides, because a thickness difference between portions ina vicinity of the optical axis and in a vicinity of a periphery of thelens element in the eighth embodiment is less than that of the firstembodiment, the ocular optical system in the eighth embodiment is, incomparison with that provided in the first embodiment, easier to bemanufactured and thus has higher yield.

FIG. 39 is a schematic view illustrating an ocular optical systemaccording to the ninth embodiment of the invention, and FIG. 40A to FIG.40D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the ninth embodiment of theinvention. With reference to FIG. 39, the ocular optical system 10according to the ninth embodiment of the invention is similar to thatprovided in the first embodiment, while the differences therebetween areas follows. The optical data, the aspheric coefficients, and theparameters of the lens elements 3, 4, and 5 in these two embodiments aredifferent to some extent. Moreover, in this embodiment, the eye-sidesurface 31 of the first lens element 3 has a concave portion 312 in avicinity of the optical axis I and a convex portion 313 in a vicinity ofa periphery of the first lens element 3. The display-side surface 42 ofthe second lens element 4 has a concave portion 422 in a vicinity of theoptical axis I and a convex portion 423 in a vicinity of a periphery ofthe second lens element 4. The eye-side surface 51 of the third lenselement 5 is a concave surface, and has a concave portion 512 in avicinity of the optical axis I and a concave portion 514 in a vicinityof a periphery of the third lens element 5. The display-side surface 52of the third lens element 5 is a convex surface, and has a convexportion 521 in a vicinity of the optical axis I and a convex portion 523in a vicinity of a periphery of the third lens element 5. For clearillustration, it should be mentioned that the same reference numbers ofthe concave portions and the convex portions in the two embodiments areomitted from FIG. 39. In this embodiment, all the eye-side surfaces 31,41, and 51 and all the display-side surfaces 32, 42, and 52 are asphericsurfaces.

Detailed optical data of the ocular optical system 10 in the ninthembodiment are indicated in FIG. 41. In the ninth embodiment, EFL of theocular optical system 10 is 51.558 mm, ω thereof is 45.000°, TTL thereofis 61.921 mm, Fno thereof is 8.324, and 0.5 times DLD thereof is 35.043mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 42 according to the ninth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the ninth embodiment is indicated inFIG. 45 and FIG. 46.

In FIG. 40A which illustrates the longitudinal spherical aberration whenthe pupil radius is 3.0000 mm according to the ninth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±1.4 mm. In FIG. 40B and FIG. 40C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±1.2 mm. In FIG. 40D, thediagram of distortion aberration shows that the distortion aberration inthe ninth embodiment can be maintained within the range of ±32%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the ninth embodiment can have the favorableimaging quality, given that TTL is shortened to about 61.921 mm.

According to the above description, compared to the first embodiment,the advantages of the ninth embodiment are as follows. Fno of the ninthembodiment is less than that of the first embodiment. ω of the ninthembodiment is less than that of the first embodiment. The fieldcurvature of the ninth embodiment is less than that of the firstembodiment. Besides, because a thickness difference between portions ina vicinity of the optical axis and in a vicinity of a periphery of thelens element in the ninth embodiment is less than that of the firstembodiment, the ocular optical system in the ninth embodiment is, incomparison with that provided in the first embodiment, easier to bemanufactured and thus has higher yield.

FIG. 43 to FIG. 46 are table diagrams showing the optical parametersprovided in the foregoing nine embodiments. If the relationship amongthe optical parameters in the ocular optical system 10 provided in theembodiments of the invention satisfies at least one of the followingconditions, the design of the ocular optical system with favorableoptical performance, the reduced length in whole, and effectivelyincreased apparent field of view becomes technical feasible:

1. To achieve the reduced system length of the ocular optical system 10and the effectively increased apparent field of view, the thicknesses ofthe lens elements and the air gaps between the lens elements may beappropriately reduced. However, when the difficulty of assembling thelens elements and image quality are considered, the thicknesses of thelens elements and the air gaps are needed to be adjusted to one another.Therefore, when at least one of the following conditions are satisfied,the ocular optical system 10 may be arranged well:

(a) 1.0≤TTL/G3D is satisfied, preferably 1.0≤TTL/G3D≤4.5 is satisfied.When 1.0≤TTL/G3D≤1.5 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 1.5≤TTL/G3D≤4.5 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(b) 0.5≤(T1+G12)/T2 is satisfied, preferably 0.50≤(T1+G12)/T2≤4.50.

(c) 1.5≤TTL/(T1+T2) is satisfied, preferably 1.50≤TTL/(T1+T2)≤6.00 issatisfied. When 3.0≤TTL/(T1+T2)≤6.0 is satisfied, the distortion andastigmatic aberration are obviously reduced. When 1.5≤TTL/(T1+T2)≤3.0 issatisfied, the longitudinal spherical aberration is obviously reduced.

(d) 2.5≤TTL/(T2+T3) is satisfied, preferably 2.50≤TTL/(T2+T3)≤9.00 issatisfied.

(e) 3.0≤TTL/(G23+T3) is satisfied, preferably 3.00≤TTL/(G23+T3)≤23.00 issatisfied. When 6.0≤TTL/(G23+T3)≤23.0 is satisfied, the distortion andastigmatic aberration are obviously reduced. When 3.0≤TTL/(G23+T3)≤6.0is satisfied, the longitudinal spherical aberration is obviouslyreduced.

(f) 1.0≤D1/T1 is satisfied, preferably 1.00≤D1/T1≤5.00 is satisfied.When 4.0≤D1/T1≤5.0 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 1.0≤D1/T1≤4.0 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(g) 2.0≤D2/T2 is satisfied, preferably 2.00≤D2/T2≤19.00 is satisfied.

(h) 6.0≤D3/T3 is satisfied, preferably 6.00≤D3/T3≤21.00 is satisfied.

(i) T1/T2≤6 is satisfied, preferably 0.50≤T1/T2≤6.00 is satisfied. When1.4≤T1/T2≤6.0 is satisfied, the distortion and astigmatic aberration areobviously reduced. When 0.5≤T1/T2≤4.0 is satisfied, the longitudinalspherical aberration is obviously reduced.

(j) 1≤T1/(G12+T3) is satisfied, preferably 1.00≤T1/(G12+T3)≤8.00 issatisfied. When 1.0≤T1/(G12+T3)≤3.0 is satisfied, the distortion andastigmatic aberration are obviously reduced. When 3.0≤T1/(G12+T3)≤8.0,the longitudinal spherical aberration is obviously reduced.

(k) 0.25≤T2/(G12+T3) is satisfied, preferably 0.25≤T2/(G12+T3)≤8.00 issatisfied. When 0.25≤T2/(G12+T3)≤2.0 is satisfied, the distortion andastigmatic aberration are obviously reduced. When 1.4≤T2/(G12+T3)≤8.0 issatisfied, the longitudinal spherical aberration is obviously reduced.

(l) G3D/T1≤7 is satisfied, preferably 0.5≤G3D/T1≤7.00 is satisfied. When4.0≤G3D/T1≤7.0 is satisfied, the distortion and astigmatic aberrationare obviously reduced. When 0.5≤G3D/T1≤1.5 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(m) G3D/T2≤22 is satisfied, preferably 0.9≤G3D/T2≤22.00 is satisfied.When 7.0≤G3D/T2≤22.0 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 0.9≤G3D/T2≤3.0 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(n) 3≤G3D/T3 is satisfied, preferably 3.0≤G3D/T3≤18.00 is satisfied.When 5.0≤G3D/T3≤18.0 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 3.0≤G3D/T3≤8.0 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(o) G3D/Gaa≤430 is satisfied, preferably 1.0≤G3D/Gaa≤430.00 issatisfied. When 30.0≤G3D/Gaa≤430.0 is satisfied, the distortion andastigmatic aberration are obviously reduced. When 1.0≤G3D/Gaa≤2.4 issatisfied, the longitudinal spherical aberration is obviously reduced.

(p) G3D/ALT≤3.5 is satisfied, preferably 0.4≤G3D/ALT≤3.5 is satisfied.When 2.00≤G3D/ALT≤3.5 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 0.4≤G3D/ALT≤0.8 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(q) SL/T1≤11 is satisfied, preferably 3.0 SL/T1≤11.0 is satisfied. When8.00≤SL/T1≤11.0 is satisfied, the distortion and astigmatic aberrationare obviously reduced. When 3.0≤SL/T1≤6.0 is satisfied, the longitudinalspherical aberration is obviously reduced.

2. Adjusting EFL facilitates increasing the apparent field of view. Ifat least one of the following conditions is satisfied, when the systemlength of the ocular optical system 10 is reduced, the apparent field ofview is also increased:

(a) 1.0≤EFL/(T1+G12+T2) is satisfied, preferably1.00≤EFL/(T1+G12+T2)≤4.50 is satisfied. When 2.0≤EFL/(T1+G12+T2)≤4.5 issatisfied, the distortion and astigmatic aberration are obviouslyreduced. When 1.0≤EFL/(T1+G12+T2)≤2.0 is satisfied, the longitudinalspherical aberration is obviously reduced.

(b) 2.0≤EFL/T1 is satisfied, preferably 2.00≤EFL/T1≤7.00 is satisfied.When 5.0≤EFL/T1≤7.0 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 2.0≤EFL/T1≤5.0 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(c) 2.5≤EFL/T2 is satisfied, preferably 2.50≤EFL/T2≤25.00 is satisfied.When 10.0≤EFL/T2≤25.0 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 2.5≤EFL/T2≤10.0 is satisfied, thelongitudinal spherical aberration is obviously reduced.

3. To keep the eye relief ER and various optical parameters to suitablevalues, at least one of the following conditions may be satisfied, so asto prevent the slimness of the ocular optical system 10 in whole frombeing affected by any overly large parameter, or prevent the assemblyfrom being affected or the manufacturing difficulty from increased bythe any overly small parameter:

(a) 0.5≤ALT/ER is satisfied, preferably 0.50≤ALT/ER≤3.00 is satisfied.When 0.5≤ALT/ER≤1.5 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 1.5≤ALT/ER≤3.0 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(b) 3.5≤TTL/ER is satisfied, preferably 3.50≤TTL/ER≤5.50 is satisfied.When 3.5≤TTL/ER≤4.5 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 4.5≤TTL/ER≤5.5 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(c) 1.1≤G3D/ER is satisfied, preferably 1.10≤G3D/ER≤3.50 is satisfied.When 2.5≤G3D/ER≤3.5 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 1.1≤G3D/ER≤2.0 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(d) ER/T1≤2.3 is satisfied, preferably 0.50≤ER/T1≤2.30 is satisfied.When 1.5≤ER/T1≤2.3 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 0.5≤ER/T1≤1.2 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(e) ER/T2≤8 is satisfied, preferably 0.60≤ER/T2≤8.00 is satisfied. When2.5≤ER/T2≤8.0 is satisfied, the distortion and astigmatic aberration areobviously reduced. When 0.6≤ER/T2≤2.5 is satisfied, the longitudinalspherical aberration is obviously reduced.

(f) 2≤ER/T3 is satisfied, preferably 2.00≤ER/T3≤7.00 is satisfied. When2.0≤ER/T3≤6.0 is satisfied, the distortion and astigmatic aberration areobviously reduced. When 2.5≤ER/T3≤5.0 is satisfied, the longitudinalspherical aberration is obviously reduced.

(g) EFL/ER≤4.5 is satisfied, preferably 2.00≤EFL/ER≤4.50 is satisfied.When 3.5≤EFL/ER≤4.5 is satisfied, the longitudinal spherical aberrationis obviously reduced.

4. By limiting the magnitude relationship between EPSD and variousoptical parameters, the half apparent field of view is not so small thatcan cause narrow vision:

(a) DLD/EPSD≤36 is satisfied, preferably 20.0≤DLD/EPSD≤36.00 issatisfied. When 20.0≤DLD/EPSD≤28.0 is satisfied, the distortion andastigmatic aberration are obviously reduced. When 22.0≤DLD/EPSD≤36.0 issatisfied, the longitudinal spherical aberration is obviously reduced.Moreover, when 6≤0.5DLD/EPSD≤20, the aberration may be also obviouslyreduced.

(b) DLD/G3D≤5 is satisfied, preferably 1.30≤DLD/G3D≤5.00 is satisfied.When 1.3≤DLD/G3D≤2.2 is satisfied, the distortion and astigmaticaberration are obviously reduced. When 3.3≤DLD/G3D≤5.0 is satisfied, thelongitudinal spherical aberration is obviously reduced.

(c) EFL/DLD≤0.8 is satisfied, preferably 0.6≤EFL/DLD≤0.80 is satisfied.When 0.65 EFL/DLD≤0.75 is satisfied, the longitudinal sphericalaberration is obviously reduced.

5. When the ocular optical system 10 satisfies f2/f1≤15, in thecondition that the second lens element 4 corrects the aberration of thefirst lens element 3, the EFL of the ocular optical system 10 and themagnifying power are not overly affected. Preferably, (−3)≤f2/f1≤15 issatisfied, so as to prevent the refracting power of the second lenselement 4 from being so small that is not enough to correct theaberration of the first lens element 3. When (−3.0)≤f2/f1≤3.0 issatisfied, the distortion and astigmatic aberration are obviouslyreduced. When 3.0≤f2/f1≤15.0 is satisfied, the longitudinal sphericalaberration is obviously reduced.

6. Because 250 mm is the least distance of distinct vision of youngpeople (the closest distance that the eye of young people is able toclearly focus on), the magnifying power of the system can approach aratio of 250 millimeter (mm) and G3D. Therefore, if 250 mm/G3D≤25 can besatisfied, the magnifying power of the system is unlikely to be so largethat can increase the thickness and manufacturing difficulty of the lenselement. If 2.5≤250 mm/G3D≤25 can be further satisfied, G3D is unlikelyto be so long that can affect the system length. When 2.5≤250mm/G3D≤10.0 is satisfied, the distortion and astigmatic aberration areobviously reduced. When 10.0≤250 mm/G3D≤25.0 is satisfied, thelongitudinal spherical aberration is obviously reduced.

7. When at least one of the following conditions is satisfied, thedefinition of local image of the object is effectively enhanced, and theaberration of the local image of the object is effected corrected:

(a) 0.8≤v1/v2 is satisfied, preferably 0.80≤v1/v2≤3.0 is satisfied. When0.8≤v1/v2≤1.2 is satisfied, the longitudinal spherical aberration isobviously reduced.

(b) For the second embodiment, both| v1−v2|≥20 and | v1−v3|≤5 aresatisfied, which can effectively correct the aberration of local imageof the object. For the other embodiments, both| v1−v2|≤5 and | v1−v3|≥20are satisfied, which can effectively correct the aberration of localimage of the object.

8. If the following condition can be satisfied, the observer mayexperience immersion feeling: 40°≤ω.

9. If the system can satisfy at least one of the following conditions:0.69≤(ER+G12+T3)/T1≤2.09, 0.79≤(ER+G12+T3)/T2≤3.25,0.99≤(ER+G12+T3)/G23≤16.16, 0.38≤(ER+G12+T3)/G3D≤1.02,1.27≤(ER+G12+G3D)/T1≤7.19, 1.71≤(ER+G12+G3D)/T2≤11.19,1.81≤(ER+G12+G3D)/Gaa≤49.2, 1.03≤(ER+T2+T3)/T1≤2.72,0.49≤(ER+T2+T3)/G3D≤1.71, 1.84≤(ER+T3+G3D)/T2≤11.72,0.7≤(ER+G23+ALT)/G3D≤3.82, 0.43≤(ER+T2+Gaa)/G3D≤2.23, and0.7≤(ER+TL)/G3D≤3.82, the exit pupil distance and various opticalparameters can be maintained at appropriate values, so as to prevent anyparameter from being so large that can cause the distance between theeye and the ocular optical system 10 to be so large or small that canmake the eye uncomfortable, or prevent the assembly from being affectedor the manufacturing difficulty from increased by the any overly smallparameter.

10. If the system can satisfy at least one of the following conditions:1.06≤(ER+G12+T3)/T1≤2.77, 0.79≤(ER+G12+T3)/T2≤11.05,1.63≤(ER+G12+T3)/G23≤55.25, 0.38≤(ER+G12+T3)/G3D≤0.83,2.08≤(ER+G12+G3D)/T1≤7.19, 1.71≤(ER+G12+G3D)/T2≤27.55,3.49≤(ER+G12+G3D)/Gaa≤110.2, 2.1≤(ER+T2+T3)/T1≤3,1.84≤(ER+T3+G3D)/T2≤31, 0.7=(ER+G23+ALT)/G3D≤2.87,0.43≤(ER+T2+Gaa)/G3D≤2.05, and 0.7≤(ER+TL)/G3D≤2.87, the field curvatureis reduced.

11. If the system can satisfy at least one of the following conditions:2.08≤(ER+G12+T3)/T1≤2.77, 3.24≤(ER+G12+T3)/T2≤11.05,16.15≤(ER+G12+T3)/G23≤55.25, 0.38≤(ER+G12+T3)/G3D≤0.56,6.88≤(ER+G12+G3D)/T1≤7.19, 11.18≤(ER+G12+G3D)/T2≤27.55,49.19≤(ER+G12+G3D)/Gaa≤110.2, 2.71≤(ER+T2+T3)/T1≤3,0.49≤(ER+T2+T3)/G3D≤0.6, 11.71≤(ER+T3+G3D)/T2≤31,0.7≤(ER+G23+ALT)/G3D≤0.81, 0.43≤(ER+T2+Gaa)/G3D≤0.46, and0.7≤(ER+TL)/G3D≤0.82, the longitudinal spherical aberration is reduced.

12. If the system can satisfy at least one of the following conditions:1.1≤TTL/EFL≤1.29, 1.34≤SL/EFL≤1.63, 1.35≤DLD/EFL≤1.47, and1.2≤(T1+G23)/T2≤6.06, the EFL and various optical parameters can bemaintained at an appropriate value, so as to prevent the aberrationcorrection of the ocular optical system 10 in whole from being affectedby any overly large parameter, or prevent the assembly from beingaffected or the manufacturing difficulty from increased by the anyoverly small parameter. When at least one of 1.2≤TTL/EFL≤1.29,1.43≤SL/EFL≤1.63, 1.29≤DLD/EFL≤1.47, and 1.2≤(T1+G23)/T2≤4.2 issatisfied, the field curvature is reduced. When 1.75≤(T1+G23)/T2≤4.2 issatisfied, the longitudinal spherical aberration is reduced.

However, due to the unpredictability of the design of an optical system,with the framework set forth in the embodiments of the invention, theocular optical system satisfying said conditions can be characterized bythe reduced system length, the enlarged available aperture, theincreased apparent field of view, ER>8 mm, the improved imaging quality,or the improved assembly yield, such that the shortcomings described inthe related art can be better prevented.

To sum up, the ocular optical system 10 described in the embodiments ofthe invention may have at least one of the following advantages and/orachieve at least one of the following effects.

1. The longitudinal spherical aberrations, field curvature aberrations,and distortion aberrations provided in the embodiments of the inventionall comply with usage specifications. Moreover, the off-axis rays withdifferent heights and the three representative wavelengths (450 nm, 540nm, and 630; or 486 nm, 587 nm, and 656 nm) are all gathered aroundimaging points, and according to a deviation range of each curve, it canbe observed that deviations of the imaging points of the off-axis rayswith different heights are all controlled and thus capable ofsuppressing spherical aberrations, image aberrations, and distortion.With reference to the imaging quality data, distances among the threerepresentative wavelengths (450 nm, 540 nm, and 630; or 486 nm, 587 nm,and 656 nm) are fairly close, which indicates that rays with differentwavelengths in the embodiments of the invention can be well concentratedunder different circumstances to provide the capability of suppressingdispersion. As such, it can be known from the above that, theembodiments of the invention can provide favorable optical properties.

2. Having the feature of the first lens element 3 having positiverefracting power, the display-side surface 42 of the second lens element4 having a convex portion 421 in a vicinity of the optical axis I, andthe eye-side surface 51 of the third lens element 5 having a convexportion 511 in a vicinity of the optical axis I with the feature of theeye-side surface 41 of the second lens element 4 having a convex portion411 in a vicinity of the optical axis or the feature of the eye-sidesurface 41 of the second lens element 4 having a convex portion 413 in avicinity of a periphery of the second lens element 4 facilitatesreducing field curvature. Alternatively, having the feature of thedisplay-side surface 42 of the second lens element 4 having a convexportion 421 in a vicinity of the optical axis I and the eye-side surface51 of the third lens element 5 having a convex portion 511 in a vicinityof the optical axis I and a convex portion 513 in a vicinity of aperiphery of the third lens element 5 with the feature of the third lenselement 5 having negative refracting power, the display-side surface 52of the third lens element 5 having a concave portion 522 in a vicinityof the optical axis I, or the display-side surface 52 of the third lenselement 5 having a concave portion 524 in a vicinity of a periphery ofthe third lens element 5 also facilitates reducing field curvature.Having the feature of the eye-side surface 41 of the second lens element4 having a convex portion 411 in a vicinity of the optical axis I, theeye-side surface 51 of the third lens element 5 having a convex portion511 in a vicinity of the optical axis I, and the display-side surface 52of the third lens element 5 having a concave portion 524 in a vicinityof a periphery of the third lens element 5 with the feature of thesecond lens element 4 having positive refracting power, the display-sidesurface 42 of the second lens element 4 having a convex portion 421 in avicinity of the optical axis I, the display-side surface 42 of thesecond lens element 4 having a convex portion 423 in a vicinity of aperiphery of the second lens element 4, or the third lens element 5having negative refracting power facilitates reducing the distortion.

3. Having the feature of the eye-side surface 31 of the first lenselement 3 having a concave portion 312 in a vicinity of the optical axisI with the feature of the display-side surface 52 of the third lenselement 5 having a convex portion 523 in a vicinity of a periphery ofthe third lens element 5 facilitates reducing the field curvature.Having the feature of the eye-side surface 31 of the first lens element3 having a concave portion 312 in a vicinity of the optical axis I withthe feature of the eye-side surface 41 of the second lens element 4having a concave portion 414 in a vicinity of a periphery of the secondlens element 4 or the eye-side surface 51 of the third lens element 5having a convex portion 511 in a vicinity of the optical axis Ifacilitates reducing the longitudinal spherical aberration. Having thefeature of the eye-side surface 31 of the first lens element 3 having aconcave portion 312 in a vicinity of the optical axis I with the featureof the eye-side surface 31 of the first lens element 3 having a convexportion 313 in a vicinity of a periphery of the first lens element 3,the second lens element 4 having negative refracting power, the eye-sidesurface 41 of the second lens element 4 having a concave portion 412 ina vicinity of the optical axis I, the third lens element 5 havingpositive refracting power, or the eye-side surface 51 of the third lenselement 5 having a convex portion 513 in a vicinity of a periphery ofthe third lens element 5 facilitates the imaging rays entering the eyeto form an image.

4. Having the feature of the display-side surface 42 of the second lenselement 4 having a concave portion 422 in a vicinity of the optical axisI with the feature of the second lens element 4 having positiverefracting power facilitates reducing the distortion. Having the featureof the display-side surface 42 of the second lens element 4 having aconcave portion 422 in a vicinity of the optical axis I and the eye-sidesurface 41 of the second lens element 4 having a convex portion 411 in avicinity of the optical axis I with the feature of the third lenselement 5 having negative refracting power or the eye-side surface 51 ofthe third lens element 5 having a concave portion 514 in a vicinity of aperiphery of the third lens element 5 facilitates reducing thelongitudinal spherical aberration. Having the feature of the eye-sidesurface 41 of the second lens element 4 having a convex portion 411 in avicinity of the optical axis, the display-side surface 42 of the secondlens element 4 having a concave portion 422 in a vicinity of the opticalaxis I, and the eye-side surface 51 of the third lens element 5 having aconcave portion 512 in a vicinity of the optical axis I, or the featureof the eye-side surface 41 of the second lens element 4 having a convexportion 411 in a vicinity of the optical axis I, the eye-side surface 51of the third lens element 5 having a concave portion 512 in a vicinityof the optical axis I, and the display-side surface 52 of the third lenselement 5 having a convex portion 521 in a vicinity of the optical axisI facilitates reducing the field curvature.

5. In addition, system limitations may be further added by using anycombination relation of the parameters selected from the providedembodiments to implement the system design with the same framework setforth in the embodiments of the invention. In view of theunpredictability of the design of an optical system, with the frameworkset forth in the embodiments of the invention, the ocular optical systemsatisfying said conditions can be characterized by the reduced systemlength, the enlarged exit pupil diameter, the improved imaging quality,or the improved assembly yield, such that the shortcomings described inthe related art can be better prevented.

6. The aforementioned limitation relations are provided in an exemplarysense and can be randomly and selectively combined and applied to theembodiments of the invention in different manners; the invention shouldnot be limited to the above examples. In implementation of theinvention, apart from the above-described relations, it is also possibleto add additional detailed structure such as more concave and convexcurvatures arrangement of a specific lens element or a plurality of lenselements so as to enhance control of system property and/or resolution.For example, it is optional to form an additional convex portion in thevicinity of the optical axis on the eye-side surface of the first lenselement. It should be noted that the above-described details can beoptionally combined and applied to the other embodiments of theinvention under the condition where they are not in conflict with oneanother.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the structure of the presentinvention without departing from the scope or spirit of the invention.In view of the foregoing, it is intended that the present inventioncover modifications and variations of this invention provided they fallwithin the scope of the following claims and their equivalents.

What is claimed is:
 1. An ocular optical system, for imaging of imaging rays entering an eye of an observer via the ocular optical system from a display screen, a side facing towards the eye being an eye-side, a side facing towards the display screen being a display-side, the ocular optical system comprising a first lens element, a second lens element, and a third lens element from the eye-side to the display-side in order along an optical axis, the first lens element, the second lens element, and the third lens element each comprising an eye-side surface and a display-side surface, wherein lens elements having refracting power of the ocular optical system are only the first lens element, the second lens element, and the third lens element, wherein the ocular optical system satisfies: 1.40≤T2/(G12+T3)≤8.00 and 2.50≤TTL/(T2+T3)≤9.00, where T2 is a thickness of the second lens element along the optical axis, T3 is a thickness of the third lens element along the optical axis, G12 is an air gap from the first lens element to the second lens element along the optical axis, and TTL is a distance from the eye-side surface of the first lens element to the display screen along the optical axis.
 2. The ocular optical system according to claim 1, wherein the ocular optical system satisfies: 3.00≤TTL/(G23+T3)≤23.00, where G23 is an air gap from the second lens element to the third lens element along the optical axis.
 3. The ocular optical system according to claim 1, wherein the ocular optical system satisfies: 1.0≤D1/T1, where D1 is a diameter of a clear aperture of the eye-side surface of the first lens element, and T1 is a thickness of the first lens element along the optical axis.
 4. The ocular optical system according to claim 1, wherein the ocular optical system satisfies: 0.90≤G3D/T2≤3.00, where G3D is a distance from the third lens element to the display screen along the optical axis.
 5. The ocular optical system according to claim 1, wherein the ocular optical system satisfies: 1.00≤EFL/(T1+G12+T2)≤2.00, where EFL is an effective focal length of the ocular optical system, and T1 is a thickness of the first lens element along the optical axis.
 6. The ocular optical system according to claim 1, wherein the ocular optical system satisfies: 2.00≤EFL/T1≤5.00, where EFL is an effective focal length of the ocular optical system, and T1 is a thickness of the first lens element along the optical axis.
 7. The ocular optical system according to claim 1, wherein the ocular optical system satisfies: 2.50≤EFL/T2≤10.00, where EFL is an effective focal length of the ocular optical system.
 8. An ocular optical system, for imaging of imaging rays entering an eye of an observer via the ocular optical system from a display screen, a side facing towards the eye being an eye-side, a side facing towards the display screen being a display-side, the ocular optical system comprising a first lens element, a second lens element, and a third lens element from the eye-side to the display-side in order along an optical axis, the first lens element, the second lens element, and the third lens element each comprising an eye-side surface and a display-side surface, wherein lens elements having refracting power of the ocular optical system are only the first lens element, the second lens element, and the third lens element, wherein the ocular optical system satisfies: 0.25≤T2/(G12+T3), 2.50≤TTL/(T2+T3) and 40°≤ω, where ω represents a half apparent field of view, which is one half the field of view of the observer, TTL is a distance from the eye-side surface of the first lens element to the display screen along the optical axis, T2 is a thickness of the second lens element along the optical axis, T3 is a thickness of the third lens element along the optical axis, and G12 is an air gap from the first lens element to the second lens element along the optical axis.
 9. The ocular optical system according to claim 8, wherein the ocular optical system satisfies: 1.50≤TTL/G3D, where G3D is a distance from the third lens element to the display screen along the optical axis.
 10. The ocular optical system according to claim 8, wherein the ocular optical system satisfies: 2.00≤D2/T2, where D2 is a diameter of a clear aperture of the eye-side surface of the second lens element.
 11. The ocular optical system according to claim 8, wherein the ocular optical system satisfies: 1.50≤TTL/(T1+T2)≤6.00, where T1 is a thickness of the first lens element along the optical axis.
 12. The ocular optical system according to claim 8, wherein the ocular optical system satisfies: 0.60≤ER/T2≤2.50, where ER is a distance from a pupil of the eye of the observer to the first lens element along the optical axis.
 13. The ocular optical system according to claim 8, wherein the ocular optical system satisfies: 0.50≤(T1+G12)/T2≤4.50, where T1 is a thickness of the first lens element along the optical axis.
 14. The ocular optical system according to claim 8, wherein the ocular optical system satisfies: 0.50≤T1/T2≤4.00, where T1 is a thickness of the first lens element along the optical axis.
 15. An ocular optical system, for imaging of imaging rays entering an eye of an observer via the ocular optical system from a display screen, a side facing towards the eye being an eye-side, a side facing towards the display screen being a display-side, the ocular optical system comprising a first lens element, a second lens element, and a third lens element from the eye-side to the display-side in order along an optical axis, the first lens element, the second lens element, and the third lens element each comprising an eye-side surface and a display-side surface, wherein lens elements having refracting power of the ocular optical system are only the first lens element, the second lens element, and the third lens element, wherein the ocular optical system satisfies: 0.25≤T2/(G12+T3), 2.50≤TTL/(T2+T3), 3.00≤G3D/T3, ER/T2≤8, and 1.34≤SL/EFL≤1.63, where T2 is a thickness of the second lens element along the optical axis, T3 is a thickness of the third lens element along the optical axis, G12 is an air gap from the first lens element to the second lens element along the optical axis, TTL is a distance from the eye-side surface of the first lens element to the display screen along the optical axis, G3D is a distance from the third lens element to the display screen along the optical axis, ER is a distance from a pupil of the eye of the observer to the first lens element along the optical axis, SL represents a system length, which is a distance from a pupil of the observer to the display screen along the optical axis, and EFL is an effective focal length of the ocular optical system.
 16. The ocular optical system according to claim 15, wherein the ocular optical system satisfies: 6.00≤D3/T3, where D3 is a diameter of a clear aperture of the eye-side surface of the third lens element.
 17. The ocular optical system according to claim 15, wherein the ocular optical system satisfies: 2.50≤ER/T3≤5.00.
 18. The ocular optical system according to claim 15, wherein the ocular optical system satisfies: 22.00≤DLD/EPSD≤36.00, where DLD is a diagonal length of the display screen corresponding to one single pupil of the observer, and EPSD is a semidiameter of the single pupil of the observer.
 19. The ocular optical system according to claim 15, wherein the ocular optical system satisfies: 2.50≤250/G3D≤25.00.
 20. The ocular optical system according to claim 15, wherein the ocular optical system satisfies: 0.80≤v1/v2≤1.20, where v1 is an Abbe number of the first lens element, and v2 is an Abbe number of the second lens element. 